Subgroups — C₄₁×#61431 #23837632

Order 10496.

2000 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3481	C₂	1	2	yes	maximal, complemented
2	C₄₁×#3396	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3361	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3339	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3338	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#3297	C₂	1	4	yes	maximal, complemented
8	C₄₁×#3295	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3280	C₂	1	2	yes	maximal, complemented
10	D₄×D₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#3169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3168	C₂	1	2	yes	maximal, complemented
13	C₄₁×#3106	C₂	1	2	yes	maximal, complemented
14	C₄₁×#3105	C₂	1	4	yes	maximal, complemented
15	C₈×#41×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#135×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₄×D₈×C₄₁	C₂	1	2	yes	maximal, complemented
18	C₂×#135×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₄₁	C₂²	1	2	yes	—
20	C₄₁×#559	C₂²	1	2	yes	complemented
21	C₄₁×#554	C₂²	1	2	yes	—
22	C₄₁×#554	C₂²	1	2	yes	complemented
23	C₄₁×#553	—	2	2	no	—
24	C₄₁×#553	C₂²	1	4	yes	complemented
25	C₄₁×#551	—	2	4	no	—
26	C₄₁×#546	—	2	2	no	—
27	C₄₁×#546	C₂²	1	4	yes	complemented
28	D₄²×C₄₁	C₂²	1	2	yes	—
29	C₄₁×#532	C₂²	1	2	yes	complemented
30	C₄₁×#529	—	2	2	no	—
31	C₄₁×#529	C₂²	1	4	yes	complemented
32	C₄₁×#525	—	2	4	no	—
33	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
34	C₄×#41×C₄₁	C₂²	1	2	yes	complemented
35	C₂×C₄×D₄×C₄₁	—	2	2	no	—
36	C₂×C₄×D₄×C₄₁	C₂²	1	4	yes	complemented
37	C₄₁×#500	C₂²	1	1	yes	characteristic, complemented
38	C₄₁×#499	C₂²	1	2	yes	complemented
39	C₄₁×#495	C₂²	1	2	yes	complemented
40	C₄₁×#493	C₂²	1	1	yes	characteristic
41	C₄₁×#488	C₂²	1	4	yes	complemented
42	C₄₁×#486	C₂²	1	2	yes	complemented
43	C₄₁×#484	C₂²	1	4	yes	complemented
44	C₄₁×#482	C₂²	1	4	yes	complemented
45	C₄₁×#481	C₂²	1	4	yes	complemented
46	C₄₁×#478	C₂²	1	4	yes	complemented
47	C₄₁×#478	C₂²	1	4	yes	complemented
48	C₄₁×#477	C₂²	1	2	yes	complemented
49	C₄₁×#476	C₂²	1	2	yes	complemented
50	C₄₁×#467	C₂²	1	2	yes	complemented
51	C₄₁×#466	C₂²	1	2	yes	—
52	C₄₁×#466	C₂²	1	2	yes	complemented
53	C₄₁×#466	C₂²	1	2	yes	complemented
54	C₄₁×#465	C₂²	1	4	yes	complemented
55	C₄₁×#463	C₂²	1	4	yes	complemented
56	C₄₁×#463	C₂²	1	4	yes	complemented
57	C₄₁×#460	C₂²	1	2	yes	complemented
58	C₄₁×#459	C₂²	1	2	yes	—
59	C₄₁×#450	C₂²	1	4	yes	complemented
60	C₄₁×#449	C₂²	1	4	yes	complemented
61	C₄₁×#447	C₂²	1	4	yes	—
62	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
63	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
64	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
65	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
66	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
67	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	complemented
68	C₄×SD₁₆×C₄₁	C₂²	1	4	yes	complemented
69	C₄×D₈×C₄₁	C₂²	1	2	yes	—
70	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
71	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
72	C₄×D₈×C₄₁	C₂²	1	4	yes	complemented
73	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
74	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
75	C₄×D₈×C₄₁	C₂²	1	4	yes	complemented
76	C₄×D₈×C₄₁	C₂²	1	2	yes	complemented
77	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
78	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
79	C₈×D₄×C₄₁	C₂²	1	2	yes	complemented
80	C₈×D₄×C₄₁	C₂²	1	2	yes	complemented
81	C₄₁×#431	C₂²	1	2	yes	complemented
82	C₄₁×#431	C₂²	1	1	yes	characteristic, complemented
83	C₄₁×#427	C₂²	1	1	yes	characteristic, complemented
84	C₂×#107×C₄₁	C₂²	1	2	yes	complemented
85	C₄₁×#416	C₂²	1	2	yes	complemented
86	C₂×#102×C₄₁	C₂²	1	4	yes	complemented
87	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	complemented
88	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
89	C₂×#41×C₄₁	—	2	2	no	—
90	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
91	C₂×#41×C₄₁	C₂³	1	2	yes	—
92	C₂²×D₄×C₄₁	—	2	2	no	—
93	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
94	C₂³×C₄×C₄₁	—	2	4	no	—
95	#135×C₄₁	—	2	4	no	—
96	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
97	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
98	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
99	C₂×D₈×C₄₁	—	2	8	no	—
100	C₂×D₈×C₄₁	C₂³	1	4	yes	—
101	C₂×D₈×C₄₁	C₂³	1	2	yes	—
102	C₂×D₈×C₄₁	C₂³	1	2	yes	—
103	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
105	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
107	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
108	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
109	#127×C₄₁	C₂³	1	2	yes	—
110	#126×C₄₁	—	2	4	no	—
111	#126×C₄₁	—	2	4	no	—
112	#125×C₄₁	—	2	2	no	—
113	#125×C₄₁	C₂³	1	4	yes	—
114	#124×C₄₁	—	2	2	no	—
115	#124×C₄₁	—	2	2	no	—
116	#124×C₄₁	C₂³	1	4	yes	—
117	#123×C₄₁	—	2	4	no	—
118	#123×C₄₁	—	2	4	no	—
119	#123×C₄₁	—	2	4	no	—
120	#123×C₄₁	—	2	4	no	—
121	C₂²⋊Q₈×C₄₁	—	2	2	no	—
122	C₂²⋊Q₈×C₄₁	—	2	4	no	—
123	C₂²⋊Q₈×C₄₁	—	2	4	no	—
124	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
125	#121×C₄₁	—	2	4	no	—
126	#121×C₄₁	—	2	2	no	—
127	#121×C₄₁	—	2	2	no	—
128	#121×C₄₁	—	2	4	no	—
129	#121×C₄₁	C₂³	1	4	yes	—
130	#121×C₄₁	C₂³	1	4	yes	—
131	#120×C₄₁	—	2	4	no	—
132	#120×C₄₁	—	2	4	no	—
133	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
134	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
135	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
136	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
137	C₄×D₄×C₄₁	—	2	2	no	—
138	C₄×D₄×C₄₁	—	2	4	no	—
139	C₄×D₄×C₄₁	—	2	2	no	—
140	C₄×D₄×C₄₁	—	2	2	no	—
141	C₄×D₄×C₄₁	—	2	2	no	—
142	C₄×D₄×C₄₁	—	2	4	no	—
143	C₄×D₄×C₄₁	—	2	2	no	—
144	C₄×D₄×C₄₁	—	2	4	no	—
145	C₄×D₄×C₄₁	—	2	4	no	—
146	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
147	C₄×D₄×C₄₁	D₄	1	2	yes	—
148	C₄×D₄×C₄₁	C₂³	1	2	yes	—
149	C₄×D₄×C₄₁	C₂³	1	4	yes	—
150	C₄×D₄×C₄₁	C₂³	1	4	yes	—
151	C₄×D₄×C₄₁	C₂³	1	4	yes	—
152	C₄×D₄×C₄₁	C₂³	1	2	yes	—
153	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
154	C₄×D₄×C₄₁	C₂³	1	2	yes	—
155	#117×C₄₁	—	2	2	no	—
156	#117×C₄₁	—	2	4	no	—
157	#117×C₄₁	D₄	1	2	yes	—
158	#117×C₄₁	D₄	1	1	yes	characteristic
159	#117×C₄₁	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
161	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
162	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
163	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
164	C₂×C₄²×C₄₁	—	2	2	no	—
165	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
166	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
167	#107×C₄₁	C₂³	1	2	yes	—
168	#107×C₄₁	C₂³	1	2	yes	—
169	#107×C₄₁	C₂³	1	1	yes	characteristic
170	#107×C₄₁	C₂³	1	4	yes	—
171	#107×C₄₁	C₂³	1	1	yes	characteristic
172	#106×C₄₁	C₂³	1	2	yes	—
173	#106×C₄₁	C₂³	1	4	yes	—
174	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
175	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
176	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
177	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
178	#103×C₄₁	C₂³	1	2	yes	—
179	#103×C₄₁	C₂³	1	2	yes	—
180	#103×C₄₁	C₂³	1	4	yes	—
181	#102×C₄₁	C₂³	1	2	yes	—
182	#102×C₄₁	C₂³	1	4	yes	—
183	#102×C₄₁	C₂³	1	4	yes	—
184	#102×C₄₁	C₂³	1	4	yes	—
185	#102×C₄₁	C₂³	1	2	yes	—
186	#102×C₄₁	C₂³	1	4	yes	—
187	#102×C₄₁	C₂³	1	4	yes	—
188	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
189	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
190	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
191	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
192	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
193	C₄×C₈×C₄₁	C₂³	1	2	yes	—
194	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₄₁	C₂³	1	2	yes	—
197	C₄×C₈×C₄₁	C₂³	1	2	yes	—
198	C₂⁴×C₄₁	—	2	4	no	—
199	#41×C₄₁	—	2	4	no	—
200	#41×C₄₁	—	2	4	no	—
201	#41×C₄₁	—	4	2	no	—
202	#41×C₄₁	—	8	4	no	—
203	C₂×Q₈×C₄₁	—	2	2	no	—
204	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
205	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
206	C₂×D₄×C₄₁	—	2	8	no	—
207	C₂×D₄×C₄₁	—	2	2	no	—
208	C₂×D₄×C₄₁	—	2	4	no	—
209	C₂×D₄×C₄₁	—	2	4	no	—
210	C₂×D₄×C₄₁	—	2	4	no	—
211	C₂×D₄×C₄₁	—	2	2	no	—
212	C₂×D₄×C₄₁	—	2	2	no	—
213	C₂×D₄×C₄₁	—	4	4	no	—
214	C₂×D₄×C₄₁	—	4	8	no	—
215	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
216	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
217	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
218	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₄₁	—	2	4	no	—
220	C₂²×C₄×C₄₁	—	2	2	no	—
221	C₂²×C₄×C₄₁	—	2	2	no	—
222	C₂²×C₄×C₄₁	—	2	2	no	—
223	C₂²×C₄×C₄₁	—	2	4	no	—
224	C₂²×C₄×C₄₁	—	2	4	no	—
225	C₂²×C₄×C₄₁	—	2	4	no	—
226	C₂²×C₄×C₄₁	—	8	8	no	—
227	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
228	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
230	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
233	Q₁₆×C₄₁	—	2	2	no	—
234	SD₁₆×C₄₁	—	2	4	no	—
235	SD₁₆×C₄₁	—	4	4	no	—
236	D₈×C₄₁	—	2	8	no	—
237	D₈×C₄₁	—	2	4	no	—
238	D₈×C₄₁	—	4	2	no	—
239	D₈×C₄₁	#41	1	4	yes	complemented
240	C₂×C₈×C₄₁	—	2	4	no	—
241	C₂×C₈×C₄₁	—	2	2	no	—
242	C₂×C₈×C₄₁	—	4	1	no	—
243	C₂×C₈×C₄₁	—	4	2	no	—
244	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
245	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
247	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
248	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
249	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
250	C₄⋊C₄×C₄₁	—	2	2	no	—
251	C₄⋊C₄×C₄₁	—	2	4	no	—
252	C₄⋊C₄×C₄₁	—	2	4	no	—
253	C₄⋊C₄×C₄₁	—	2	2	no	—
254	C₄⋊C₄×C₄₁	—	2	2	no	—
255	C₄⋊C₄×C₄₁	—	2	4	no	—
256	C₄⋊C₄×C₄₁	—	2	4	no	—
257	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
258	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
259	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
260	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
261	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
264	C₂²⋊C₄×C₄₁	—	2	4	no	—
265	C₂²⋊C₄×C₄₁	—	2	2	no	—
266	C₂²⋊C₄×C₄₁	—	2	2	no	—
267	C₂²⋊C₄×C₄₁	—	2	4	no	—
268	C₂²⋊C₄×C₄₁	—	2	4	no	—
269	C₂²⋊C₄×C₄₁	—	2	4	no	—
270	C₂²⋊C₄×C₄₁	—	2	4	no	—
271	C₂²⋊C₄×C₄₁	—	2	4	no	—
272	C₂²⋊C₄×C₄₁	—	2	2	no	—
273	C₂²⋊C₄×C₄₁	—	2	4	no	—
274	C₂²⋊C₄×C₄₁	—	2	4	no	—
275	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
276	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
277	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
278	C₄²×C₄₁	—	2	2	no	—
279	C₄²×C₄₁	—	2	2	no	—
280	C₄²×C₄₁	—	2	2	no	—
281	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₄₁	C₂×D₄	1	2	yes	—
283	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₄₁	C₂×D₄	1	2	yes	—
285	C₄²×C₄₁	C₂⁴	1	2	yes	—
286	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
287	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
288	C₂³×C₄₁	—	2	2	no	—
289	C₂³×C₄₁	—	2	4	no	—
290	C₂³×C₄₁	—	4	8	no	—
291	C₂³×C₄₁	—	4	8	no	—
292	C₂³×C₄₁	—	8	4	no	—
293	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
294	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
295	Q₈×C₄₁	—	2	2	no	—
296	Q₈×C₄₁	—	2	2	no	—
297	Q₈×C₄₁	—	2	2	no	—
298	Q₈×C₄₁	—	8	2	no	—
299	D₄×C₄₁	—	2	4	no	—
300	D₄×C₄₁	—	2	4	no	—
301	D₄×C₄₁	—	2	2	no	—
302	D₄×C₄₁	—	2	4	no	—
303	D₄×C₄₁	—	4	8	no	—
304	D₄×C₄₁	—	4	4	no	—
305	D₄×C₄₁	—	4	8	no	—
306	D₄×C₄₁	—	4	4	no	—
307	D₄×C₄₁	—	8	2	no	—
308	D₄×C₄₁	—	8	4	no	—
309	D₄×C₄₁	#135	1	4	yes	complemented
310	D₄×C₄₁	C₂×#41	1	4	yes	—
311	C₂×C₄×C₄₁	—	2	4	no	—
312	C₂×C₄×C₄₁	—	2	2	no	—
313	C₂×C₄×C₄₁	—	2	4	no	—
314	C₂×C₄×C₄₁	—	2	2	no	—
315	C₂×C₄×C₄₁	—	2	2	no	—
316	C₂×C₄×C₄₁	—	2	1	no	—
317	C₂×C₄×C₄₁	—	2	2	no	—
318	C₂×C₄×C₄₁	—	2	1	no	—
319	C₂×C₄×C₄₁	—	2	2	no	—
320	C₂×C₄×C₄₁	—	2	2	no	—
321	C₂×C₄×C₄₁	—	2	2	no	—
322	C₂×C₄×C₄₁	—	2	4	no	—
323	C₂×C₄×C₄₁	—	4	4	no	—
324	C₂×C₄×C₄₁	—	4	4	no	—
325	C₂×C₄×C₄₁	—	4	4	no	—
326	C₂×C₄×C₄₁	—	4	8	no	—
327	C₂×C₄×C₄₁	—	8	4	no	—
328	C₂×C₄×C₄₁	—	8	4	no	—
329	C₂×C₄×C₄₁	—	8	4	no	—
330	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
339	C₈×C₄₁	—	2	2	no	—
340	C₈×C₄₁	—	2	1	no	—
341	C₈×C₄₁	—	2	1	no	—
342	C₈×C₄₁	—	2	1	no	—
343	C₈×C₄₁	—	2	2	no	—
344	C₈×C₄₁	C₂×#41	1	2	yes	—
345	#61431	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
346	C₂²×C₄₁	—	2	2	no	—
347	C₂²×C₄₁	—	2	2	no	—
348	C₂²×C₄₁	—	2	1	no	—
349	C₂²×C₄₁	—	2	4	no	—
350	C₂²×C₄₁	—	2	1	no	—
351	C₂²×C₄₁	—	2	1	no	—
352	C₂²×C₄₁	—	4	2	no	—
353	C₂²×C₄₁	—	4	2	no	—
354	C₂²×C₄₁	—	4	4	no	—
355	C₂²×C₄₁	—	4	4	no	—
356	C₂²×C₄₁	—	4	4	no	—
357	C₂²×C₄₁	—	8	16	no	—
358	C₂²×C₄₁	C₂×#135	1	4	yes	—
359	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
360	C₄×C₄₁	—	2	1	no	—
361	C₄×C₄₁	—	2	2	no	—
362	C₄×C₄₁	—	2	1	no	—
363	C₄×C₄₁	—	2	2	no	—
364	C₄×C₄₁	—	2	2	no	—
365	C₄×C₄₁	—	2	1	no	—
366	C₄×C₄₁	—	4	2	no	—
367	C₄×C₄₁	—	4	2	no	—
368	C₄×C₄₁	—	4	2	no	—
369	C₄×C₄₁	—	4	4	no	—
370	C₄×C₄₁	C₂×#135	1	2	yes	—
371	C₄×C₄₁	#576	1	2	yes	—
372	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
373	C₄×C₄₁	#585	1	1	yes	characteristic
374	#3481	C₂×C₄₁	1	2	yes	complemented
375	#3396	C₂×C₄₁	1	1	yes	characteristic, complemented
376	#3380	C₂×C₄₁	1	1	yes	characteristic, complemented
377	#3361	C₂×C₄₁	1	2	yes	complemented
378	#3339	C₂×C₄₁	1	2	yes	complemented
379	#3338	C₂×C₄₁	1	1	yes	characteristic, complemented
380	#3297	C₂×C₄₁	1	4	yes	complemented
381	#3295	C₂×C₄₁	1	2	yes	complemented
382	#3280	C₂×C₄₁	1	2	yes	complemented
383	D₄×D₈	C₂×C₄₁	1	1	yes	characteristic, complemented
384	#3169	C₂×C₄₁	1	1	yes	characteristic, complemented
385	#3168	C₂×C₄₁	1	2	yes	complemented
386	#3106	C₂×C₄₁	1	2	yes	complemented
387	#3105	C₂×C₄₁	1	4	yes	complemented
388	C₈×#41	C₂×C₄₁	1	1	yes	characteristic, complemented
389	C₄×#135	C₂×C₄₁	1	1	yes	characteristic, complemented
390	C₂×C₄×D₈	C₂×C₄₁	1	2	yes	complemented
391	C₂×C₄₁	—	2	4	no	—
392	C₂×C₄₁	—	4	1	no	—
393	C₂×C₄₁	—	4	4	no	—
394	C₂×C₄₁	—	8	4	no	—
395	C₂×C₄₁	D₄×#41	1	1	yes	characteristic
396	C₂×C₄₁	C₂²×#135	1	1	yes	characteristic
397	C₂×C₄₁	C₂×#576	1	1	yes	characteristic
398	C₂×#135	C₂²×C₄₁	1	1	yes	characteristic
399	C₂²×D₈	C₂²×C₄₁	1	2	yes	—
400	#559	C₂²×C₄₁	1	2	yes	complemented
401	#554	C₂²×C₄₁	1	2	yes	—
402	#554	C₂²×C₄₁	1	2	yes	complemented
403	#553	—	2	2	no	—
404	#553	C₂²×C₄₁	1	4	yes	complemented
405	#551	—	2	4	no	—
406	#546	—	2	2	no	—
407	#546	C₂²×C₄₁	1	4	yes	complemented
408	D₄²	C₂²×C₄₁	1	2	yes	—
409	#532	C₂²×C₄₁	1	2	yes	complemented
410	#529	—	2	2	no	—
411	#529	C₂²×C₄₁	1	4	yes	complemented
412	#525	—	2	4	no	—
413	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
414	C₄×#41	C₂²×C₄₁	1	2	yes	complemented
415	C₂×C₄×D₄	—	2	2	no	—
416	C₂×C₄×D₄	C₂²×C₄₁	1	4	yes	complemented
417	#500	C₂²×C₄₁	1	1	yes	characteristic, complemented
418	#499	C₂²×C₄₁	1	2	yes	complemented
419	#495	C₂²×C₄₁	1	2	yes	complemented
420	#493	C₂²×C₄₁	1	1	yes	characteristic
421	#488	C₂²×C₄₁	1	4	yes	complemented
422	#486	C₂²×C₄₁	1	2	yes	complemented
423	#484	C₂²×C₄₁	1	4	yes	complemented
424	#482	C₂²×C₄₁	1	4	yes	complemented
425	#481	C₂²×C₄₁	1	4	yes	complemented
426	#478	C₂²×C₄₁	1	4	yes	complemented
427	#478	C₂²×C₄₁	1	4	yes	complemented
428	#477	C₂²×C₄₁	1	2	yes	complemented
429	#476	C₂²×C₄₁	1	2	yes	complemented
430	#467	C₂²×C₄₁	1	2	yes	complemented
431	#466	C₂²×C₄₁	1	2	yes	—
432	#466	C₂²×C₄₁	1	2	yes	complemented
433	#466	C₂²×C₄₁	1	2	yes	complemented
434	#465	C₂²×C₄₁	1	4	yes	complemented
435	#463	C₂²×C₄₁	1	4	yes	complemented
436	#463	C₂²×C₄₁	1	4	yes	complemented
437	#460	C₂²×C₄₁	1	2	yes	complemented
438	#459	C₂²×C₄₁	1	2	yes	—
439	#450	C₂²×C₄₁	1	4	yes	complemented
440	#449	C₂²×C₄₁	1	4	yes	complemented
441	#447	C₂²×C₄₁	1	4	yes	—
442	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
443	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
444	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
445	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
446	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
447	C₄×SD₁₆	C₂²×C₄₁	1	4	yes	complemented
448	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	complemented
449	C₄×D₈	C₂²×C₄₁	1	2	yes	—
450	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
451	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
452	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
453	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
454	C₄×D₈	C₂²×C₄₁	1	4	yes	complemented
455	C₄×D₈	C₂²×C₄₁	1	4	yes	complemented
456	C₄×D₈	C₂²×C₄₁	1	2	yes	complemented
457	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
458	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
459	C₈×D₄	C₂²×C₄₁	1	2	yes	complemented
460	C₈×D₄	C₂²×C₄₁	1	2	yes	complemented
461	#431	C₂²×C₄₁	1	2	yes	complemented
462	#431	C₂²×C₄₁	1	1	yes	characteristic, complemented
463	#427	C₂²×C₄₁	1	1	yes	characteristic, complemented
464	C₂×#107	C₂²×C₄₁	1	2	yes	complemented
465	#416	C₂²×C₄₁	1	2	yes	complemented
466	C₂×#102	C₂²×C₄₁	1	4	yes	complemented
467	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	complemented
468	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
469	C₄₁	#61431	1	1	yes	characteristic, direct product factor, Sylow
470	C₂×#41	—	2	2	no	—
471	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
472	C₂×#41	C₂³×C₄₁	1	2	yes	—
473	C₂²×D₄	—	2	2	no	—
474	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
475	C₂³×C₄	—	2	4	no	—
476	#135	—	2	4	no	—
477	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
478	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
479	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
480	C₂×D₈	—	2	8	no	—
481	C₂×D₈	C₂³×C₄₁	1	4	yes	—
482	C₂×D₈	C₂³×C₄₁	1	2	yes	—
483	C₂×D₈	C₂³×C₄₁	1	2	yes	—
484	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
485	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
486	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
487	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
488	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
489	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
490	#127	C₂³×C₄₁	1	2	yes	—
491	#126	—	2	4	no	—
492	#126	—	2	4	no	—
493	#125	—	2	2	no	—
494	#125	C₂³×C₄₁	1	4	yes	—
495	#124	—	2	2	no	—
496	#124	—	2	2	no	—
497	#124	C₂³×C₄₁	1	4	yes	—
498	#123	—	2	4	no	—
499	#123	—	2	4	no	—
500	#123	—	2	4	no	—
501	#123	—	2	4	no	—
502	C₂²⋊Q₈	—	2	2	no	—
503	C₂²⋊Q₈	—	2	4	no	—
504	C₂²⋊Q₈	—	2	4	no	—
505	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
506	#121	—	2	4	no	—
507	#121	—	2	2	no	—
508	#121	—	2	2	no	—
509	#121	—	2	4	no	—
510	#121	C₂³×C₄₁	1	4	yes	—
511	#121	C₂³×C₄₁	1	4	yes	—
512	#120	—	2	4	no	—
513	#120	—	2	4	no	—
514	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
515	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
516	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
517	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	4	no	—
520	C₄×D₄	—	2	2	no	—
521	C₄×D₄	—	2	2	no	—
522	C₄×D₄	—	2	2	no	—
523	C₄×D₄	—	2	4	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	4	no	—
526	C₄×D₄	—	2	4	no	—
527	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
528	C₄×D₄	D₄×C₄₁	1	2	yes	—
529	C₄×D₄	C₂³×C₄₁	1	2	yes	—
530	C₄×D₄	C₂³×C₄₁	1	4	yes	—
531	C₄×D₄	C₂³×C₄₁	1	4	yes	—
532	C₄×D₄	C₂³×C₄₁	1	4	yes	—
533	C₄×D₄	C₂³×C₄₁	1	2	yes	—
534	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
535	C₄×D₄	C₂³×C₄₁	1	2	yes	—
536	#117	—	2	2	no	—
537	#117	—	2	4	no	—
538	#117	D₄×C₄₁	1	2	yes	—
539	#117	D₄×C₄₁	1	1	yes	characteristic
540	#117	C₂³×C₄₁	1	2	yes	—
541	C₂×C₄⋊C₄	—	2	2	no	—
542	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
543	C₂×C₂²⋊C₄	—	2	4	no	—
544	C₂×C₂²⋊C₄	—	2	4	no	—
545	C₂×C₄²	—	2	2	no	—
546	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
547	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
548	#107	C₂³×C₄₁	1	1	yes	characteristic
549	#107	C₂³×C₄₁	1	2	yes	—
550	#107	C₂³×C₄₁	1	4	yes	—
551	#107	C₂³×C₄₁	1	1	yes	characteristic
552	#107	C₂³×C₄₁	1	2	yes	—
553	#106	C₂³×C₄₁	1	2	yes	—
554	#106	C₂³×C₄₁	1	4	yes	—
555	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
556	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
557	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
558	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
559	#103	C₂³×C₄₁	1	2	yes	—
560	#103	C₂³×C₄₁	1	2	yes	—
561	#103	C₂³×C₄₁	1	4	yes	—
562	#102	C₂³×C₄₁	1	2	yes	—
563	#102	C₂³×C₄₁	1	4	yes	—
564	#102	C₂³×C₄₁	1	4	yes	—
565	#102	C₂³×C₄₁	1	4	yes	—
566	#102	C₂³×C₄₁	1	2	yes	—
567	#102	C₂³×C₄₁	1	4	yes	—
568	#102	C₂³×C₄₁	1	4	yes	—
569	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
570	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
571	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
572	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
573	C₄×C₈	C₂³×C₄₁	1	2	yes	—
574	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
575	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
576	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
577	C₄×C₈	C₂³×C₄₁	1	2	yes	—
578	C₄×C₈	C₂³×C₄₁	1	2	yes	—
579	C₂⁴	—	2	4	no	—
580	#41	—	2	4	no	—
581	#41	—	2	4	no	—
582	#41	—	4	2	no	—
583	#41	—	8	4	no	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
586	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
587	C₂×D₄	—	2	8	no	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	4	4	no	—
595	C₂×D₄	—	4	8	no	—
596	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
597	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
598	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
599	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	8	8	no	—
608	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
609	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
610	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
611	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
614	Q₁₆	—	2	2	no	—
615	SD₁₆	—	2	4	no	—
616	SD₁₆	—	4	4	no	—
617	D₈	—	2	8	no	—
618	D₈	—	2	4	no	—
619	D₈	—	4	2	no	—
620	D₈	#41×C₄₁	1	4	yes	complemented
621	C₂×C₈	—	2	4	no	—
622	C₂×C₈	—	2	2	no	—
623	C₂×C₈	—	4	1	no	—
624	C₂×C₈	—	4	2	no	—
625	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
626	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
627	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
628	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
629	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
630	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
631	C₄⋊C₄	—	2	2	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
639	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
640	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
641	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
642	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
643	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
644	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
657	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
658	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
659	C₄²	—	2	2	no	—
660	C₄²	—	2	2	no	—
661	C₄²	—	2	2	no	—
662	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
663	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
664	C₄²	C₂×D₄×C₄₁	1	2	yes	—
665	C₄²	C₂×D₄×C₄₁	1	2	yes	—
666	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
667	C₄²	C₂⁴×C₄₁	1	2	yes	—
668	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
669	C₂³	—	2	2	no	—
670	C₂³	—	2	4	no	—
671	C₂³	—	4	8	no	—
672	C₂³	—	4	8	no	—
673	C₂³	—	8	4	no	—
674	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
675	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
676	Q₈	—	2	2	no	—
677	Q₈	—	2	2	no	—
678	Q₈	—	2	2	no	—
679	Q₈	—	8	2	no	—
680	D₄	—	2	4	no	—
681	D₄	—	2	4	no	—
682	D₄	—	2	2	no	—
683	D₄	—	2	4	no	—
684	D₄	—	4	8	no	—
685	D₄	—	4	4	no	—
686	D₄	—	4	8	no	—
687	D₄	—	4	4	no	—
688	D₄	—	8	2	no	—
689	D₄	—	8	4	no	—
690	D₄	#135×C₄₁	1	4	yes	complemented
691	D₄	C₂×#41×C₄₁	1	4	yes	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	—	4	4	no	—
706	C₂×C₄	—	4	4	no	—
707	C₂×C₄	—	4	8	no	—
708	C₂×C₄	—	8	4	no	—
709	C₂×C₄	—	8	4	no	—
710	C₂×C₄	—	8	4	no	—
711	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
712	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
713	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
714	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
715	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
716	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
717	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
718	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
719	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
720	C₈	—	2	2	no	—
721	C₈	—	2	1	no	—
722	C₈	—	2	1	no	—
723	C₈	—	2	1	no	—
724	C₈	—	2	2	no	—
725	C₈	C₂×#41×C₄₁	1	2	yes	—
726	C₂²	—	2	2	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	1	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	4	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	4	no	—
735	C₂²	—	4	4	no	—
736	C₂²	—	4	4	no	—
737	C₂²	—	8	16	no	—
738	C₂²	C₂×#135×C₄₁	1	4	yes	—
739	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
740	C₄	—	2	1	no	—
741	C₄	—	2	2	no	—
742	C₄	—	2	2	no	—
743	C₄	—	2	1	no	—
744	C₄	—	2	1	no	—
745	C₄	—	2	2	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	2	no	—
748	C₄	—	4	4	no	—
749	C₄	—	4	2	no	—
750	C₄	C₂×#135×C₄₁	1	2	yes	—
751	C₄	C₄₁×#576	1	2	yes	—
752	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
753	C₄	C₄₁×#585	1	1	yes	characteristic
754	C₂	—	2	4	no	—
755	C₂	—	4	1	no	—
756	C₂	—	4	4	no	—
757	C₂	—	8	4	no	—
758	C₂	D₄×#41×C₄₁	1	1	yes	characteristic
759	C₂	C₂²×#135×C₄₁	1	1	yes	characteristic
760	C₂	C₂×C₄₁×#576	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
socle	C₂²×C₄₁	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₄×#41×C₄₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₄₁×#3481	C₂	semidirect
2. C₄₁×#3396	C₂	semidirect
3. C₄₁×#3380	C₂	semidirect
4. C₄₁×#3361	C₂	semidirect
5. C₄₁×#3339	C₂	semidirect
6. C₄₁×#3338	C₂	semidirect
7. C₄₁×#3297	C₂	semidirect
8. C₄₁×#3295	C₂	semidirect
9. C₄₁×#3280	C₂	semidirect
10. D₄×D₈×C₄₁	C₂	semidirect
11. C₄₁×#3169	C₂	semidirect
12. C₄₁×#3168	C₂	semidirect
13. C₄₁×#3106	C₂	semidirect
14. C₄₁×#3105	C₂	semidirect
15. C₈×#41×C₄₁	C₂	semidirect
16. C₄×#135×C₄₁	C₂	semidirect
17. C₂×C₄×D₈×C₄₁	C₂	semidirect
20. C₄₁×#559	C₂²	semidirect
22. C₄₁×#554	C₂²	semidirect
24. C₄₁×#553	C₂²	semidirect
27. C₄₁×#546	C₂²	semidirect
29. C₄₁×#532	C₂²	semidirect
31. C₄₁×#529	C₂²	semidirect
34. C₄×#41×C₄₁	C₂²	semidirect
36. C₂×C₄×D₄×C₄₁	C₂²	semidirect
37. C₄₁×#500	C₂²	semidirect
38. C₄₁×#499	C₂²	semidirect
39. C₄₁×#495	C₂²	semidirect
41. C₄₁×#488	C₂²	semidirect
42. C₄₁×#486	C₂²	semidirect
43. C₄₁×#484	C₂²	semidirect
44. C₄₁×#482	C₂²	semidirect
45. C₄₁×#481	C₂²	semidirect
46. C₄₁×#478	C₂²	semidirect
47. C₄₁×#478	C₂²	semidirect
48. C₄₁×#477	C₂²	semidirect
49. C₄₁×#476	C₂²	semidirect
50. C₄₁×#467	C₂²	semidirect
52. C₄₁×#466	C₂²	semidirect
53. C₄₁×#466	C₂²	semidirect
54. C₄₁×#465	C₂²	semidirect
55. C₄₁×#463	C₂²	semidirect
56. C₄₁×#463	C₂²	semidirect
57. C₄₁×#460	C₂²	semidirect
59. C₄₁×#450	C₂²	semidirect
60. C₄₁×#449	C₂²	semidirect
62. C₈×Q₈×C₄₁	C₂²	semidirect
63. C₈×Q₈×C₄₁	C₂²	semidirect
64. C₄×Q₁₆×C₄₁	C₂²	semidirect
65. C₄×Q₁₆×C₄₁	C₂²	semidirect
66. C₄×SD₁₆×C₄₁	C₂²	semidirect
67. C₄×SD₁₆×C₄₁	C₂²	semidirect
68. C₄×SD₁₆×C₄₁	C₂²	semidirect
72. C₄×D₈×C₄₁	C₂²	semidirect
73. C₄×D₈×C₄₁	C₂²	semidirect
74. C₄×D₈×C₄₁	C₂²	semidirect
75. C₄×D₈×C₄₁	C₂²	semidirect
76. C₄×D₈×C₄₁	C₂²	semidirect
79. C₈×D₄×C₄₁	C₂²	semidirect
80. C₈×D₄×C₄₁	C₂²	semidirect
81. C₄₁×#431	C₂²	semidirect
82. C₄₁×#431	C₂²	semidirect
83. C₄₁×#427	C₂²	semidirect
84. C₂×#107×C₄₁	C₂²	semidirect
85. C₄₁×#416	C₂²	semidirect
86. C₂×#102×C₄₁	C₂²	semidirect
87. C₂×C₄×C₈×C₄₁	C₂²	semidirect
88. C₂×C₄×C₈×C₄₁	C₂²	semidirect
239. D₈×C₄₁	#41	semidirect
309. D₄×C₄₁	#135	semidirect
345. #61431	C₄₁	direct (N × H)
374. #3481	C₂×C₄₁	semidirect
375. #3396	C₂×C₄₁	semidirect
376. #3380	C₂×C₄₁	semidirect
377. #3361	C₂×C₄₁	semidirect
378. #3339	C₂×C₄₁	semidirect
379. #3338	C₂×C₄₁	semidirect
380. #3297	C₂×C₄₁	semidirect
381. #3295	C₂×C₄₁	semidirect
382. #3280	C₂×C₄₁	semidirect
383. D₄×D₈	C₂×C₄₁	semidirect
384. #3169	C₂×C₄₁	semidirect
385. #3168	C₂×C₄₁	semidirect
386. #3106	C₂×C₄₁	semidirect
387. #3105	C₂×C₄₁	semidirect
388. C₈×#41	C₂×C₄₁	semidirect
389. C₄×#135	C₂×C₄₁	semidirect
390. C₂×C₄×D₈	C₂×C₄₁	semidirect
400. #559	C₂²×C₄₁	semidirect
402. #554	C₂²×C₄₁	semidirect
404. #553	C₂²×C₄₁	semidirect
407. #546	C₂²×C₄₁	semidirect
409. #532	C₂²×C₄₁	semidirect
411. #529	C₂²×C₄₁	semidirect
414. C₄×#41	C₂²×C₄₁	semidirect
416. C₂×C₄×D₄	C₂²×C₄₁	semidirect
417. #500	C₂²×C₄₁	semidirect
418. #499	C₂²×C₄₁	semidirect
419. #495	C₂²×C₄₁	semidirect
421. #488	C₂²×C₄₁	semidirect
422. #486	C₂²×C₄₁	semidirect
423. #484	C₂²×C₄₁	semidirect
424. #482	C₂²×C₄₁	semidirect
425. #481	C₂²×C₄₁	semidirect
426. #478	C₂²×C₄₁	semidirect
427. #478	C₂²×C₄₁	semidirect
428. #477	C₂²×C₄₁	semidirect
429. #476	C₂²×C₄₁	semidirect
430. #467	C₂²×C₄₁	semidirect
432. #466	C₂²×C₄₁	semidirect
433. #466	C₂²×C₄₁	semidirect
434. #465	C₂²×C₄₁	semidirect
435. #463	C₂²×C₄₁	semidirect
436. #463	C₂²×C₄₁	semidirect
437. #460	C₂²×C₄₁	semidirect
439. #450	C₂²×C₄₁	semidirect
440. #449	C₂²×C₄₁	semidirect
442. C₈×Q₈	C₂²×C₄₁	semidirect
443. C₈×Q₈	C₂²×C₄₁	semidirect
444. C₄×Q₁₆	C₂²×C₄₁	semidirect
445. C₄×Q₁₆	C₂²×C₄₁	semidirect
446. C₄×SD₁₆	C₂²×C₄₁	semidirect
447. C₄×SD₁₆	C₂²×C₄₁	semidirect
448. C₄×SD₁₆	C₂²×C₄₁	semidirect
452. C₄×D₈	C₂²×C₄₁	semidirect
453. C₄×D₈	C₂²×C₄₁	semidirect
454. C₄×D₈	C₂²×C₄₁	semidirect
455. C₄×D₈	C₂²×C₄₁	semidirect
456. C₄×D₈	C₂²×C₄₁	semidirect
459. C₈×D₄	C₂²×C₄₁	semidirect
460. C₈×D₄	C₂²×C₄₁	semidirect
461. #431	C₂²×C₄₁	semidirect
462. #431	C₂²×C₄₁	semidirect
463. #427	C₂²×C₄₁	semidirect
464. C₂×#107	C₂²×C₄₁	semidirect
465. #416	C₂²×C₄₁	semidirect
466. C₂×#102	C₂²×C₄₁	semidirect
467. C₂×C₄×C₈	C₂²×C₄₁	semidirect
468. C₂×C₄×C₈	C₂²×C₄₁	semidirect
469. C₄₁	#61431	direct (N × H)
620. D₈	#41×C₄₁	semidirect
690. D₄	#135×C₄₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄₁×#3481	2
C₄₁×#3396	2
C₄₁×#3380	2
C₄₁×#3361	2
C₄₁×#3339	2
C₄₁×#3338	2
C₄₁×#3297	2
C₄₁×#3295	2
C₄₁×#3280	2
D₄×D₈×C₄₁	2
C₄₁×#3169	2
C₄₁×#3168	2
C₄₁×#3106	2
C₄₁×#3105	2
C₈×#41×C₄₁	2
C₄×#135×C₄₁	2
C₂×C₄×D₈×C₄₁	2
#61431	41

Subgroups — C41×#61431 #23837632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61431 #23837632